This paper is devoted to investigating the fixed-time and finite-time synchronization for fuzzy competitive neural networks with discontinuous activation functions. We introduce Filippov solution for overcoming the nonexistence of classical solutions of discontinuous system. Using the fixed-time synchronization theory, inequality technique, we obtain simple robust fixed-time synchronization conditions. Designing proper feedback controllers is a key step for the implementation of

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... Furthermore, based on the fixed-time robust synchronization, we design a switching adaptive controller and obtain the finite-time synchronization. It is noted that the settling time is independent on the initial value in the fixed-time robust synchronization. Hence, under the conditions of this paper, the considered system has better stability and feasibility. Finally, the theoretical results of this paper are attested to be indeed feasible in terms of a numerical example.